Neutrinos and Abelian Gauge Symmetries

Transcription

1 Neutrinos and Abelian Gauge Symmetries Julian Heeck ULB

2 Standard Model of Particle Physics Beautiful and simple: Julian Heeck Neutrinos and Abelian Gauge Symmetries 1/ 43

3 Standard Model of Particle Physics Not shown: Gauge group SU(3) color SU(2) isospin U(1) hypercharge ; spin-1 bosons with field strength F µν, Three copies of spin- 1 Weyl fields (families/generations) in rep. 2 Ψ 1,2,3 (3,2, 1 6 ) (3,1, 2) (3,1, 1 ) (1,2, }{{} ) (1,1,1), 2 }{{} quarks leptons One complex spin-0 field φ (1,2, 1 ) which breaks 2 SU(2) U(1) U(1) EM via φ 250GeV. About 18 free parameters, all measured as of 2013 (Brout Englert Higgs boson mass). Julian Heeck Neutrinos and Abelian Gauge Symmetries 1/ 43

4 Standard Model of Particle Physics Also not shown (because beyond SM): Neutrinos have mass and mix. Dark matter. Baryon asymmetry of our Universe. Julian Heeck Neutrinos and Abelian Gauge Symmetries 1/ 43

5 Symmetries of the Standard Model L SM renormalizable only mass dimension 4 couplings. L SM invariant under phase shifts of quarks and individual leptons. U(1) 4 : B, L e, L µ, and L τ classically conserved in the Standard Model. Nonperturbative instanton/sphaleron solutions break (B + L) = 6. U(1) B L U(1) Le L µ U(1) Lµ L τ global symmetry of quantum SM. After introducing three right-handed neutrinos ν R : U(1) B L U(1) Le L µ U(1) Lµ L τ anomaly free local symmetry. 1 (Neutrinos automatically massive due to ν R.) Breaking neutrino nature, hierarchies, mixing, baryon asymmetry,... 1 J.H., T. Araki, J. Kubo, JHEP 1207 (2012) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 2/ 43

6 Outline Unflavored Symmetries Neutrinos and abelian gauge symmetries Typically simple models: flavored {}}{ U(1) B L U(1) Le L }{{} µ U(1) Lµ L τ }{{} unflavored dark Few new particles and parameters. Renormalizable. Z gives additional pheno.. Julian Heeck Neutrinos and Abelian Gauge Symmetries 3/ 43

7 Baryon and Lepton Number Unbroken B L Majorana B L Dirac B L B and L classically conserved in the Standard Model. B +L theoretically broken non-perturbatively: (B +L) = 6. B L globally conserved. Fate of fundamental U(1) B L from experiments. Linked to neutrino nature and matter antimatter asymmetry. B L locally conserved after adding three ν R. Neutrinos massive! Three possibilities for (local) U(1) B L : 1 Unbroken B L: Dirac neutrinos + neutrinogenesis. 2 Majorana B L: (B L) = 2, Majorana ν + leptogenesis. 3 Dirac B L: (B L) = n 2, Dirac ν + Dirac leptogenesis. Julian Heeck Neutrinos and Abelian Gauge Symmetries 4/ 43

8 Unbroken B L Unflavored Symmetries Unbroken B L Majorana B L Dirac B L Almost 2 never considered, but very simple: 3 Neutrinos are Dirac, with Yukawa couplings Y ν m ν / H Baryon asymmetry via neutrinogenesis: 4 New heavy scalar doublets decay so that (B L) = L = 0, but L left = L right 0. Right-handed ν R not thermalized due to tiny Yukawas. Sphalerons only see L left, generate B via (B +L) = 6! 2 D. Feldman, P. Fileviez Perez, and P. Nath, arxiv: J.H., arxiv: K. Dick, M. Lindner, M. Ratz, and D. Wright, arxiv:hep-ph/ Julian Heeck Neutrinos and Abelian Gauge Symmetries 5/ 43

9 Signatures Unflavored Symmetries Unbroken B L Majorana B L Dirac B L No 0ν2β or other (B L) 0 processes... Z with tiny coupling α or Stückelberg mass M Z : Introduce real scalar σ with gauge trafo σ σ +M Z θ(x). ( L = 1 MZ Z µ + µ σ )( M 2 Z Z µ + ) µσ is gauge invariant (Z µ Z µ µθ). Mass term 1 2 M2 Z Z µz µ is just gauge fixing, not breaking. Abelian gauge bosons can have a mass without symmetry breaking. M Z /g not connected to m ν or leptogenesis no preferred scale! Limits from modified gravity, stellar energy losses, scattering/collider experiments, and Big Bang nucleosynthesis (ν R γ µ ν R Z µ). Unbroken (local) B L perfectly valid! 5 5 J.H., arxiv: Julian Heeck Neutrinos and Abelian Gauge Symmetries 6/ 43

10 Big Bang Nucleosynthesis Unbroken B L Majorana B L Dirac B L ν R are light (Dirac neutrinos) N eff 6 for strong Z interactions. Light Z also contributes to N eff. BBN (T 1MeV) limit: N eff < 4 at 95% C.L. 6 Thermally averaged rate via Z : Γ(ff ν R ν R ) g 4 T, M Z T, g 2 M2 Z T, M Z T, g 4 T 5, M M 4 Z T. Z rate T H T 2 1 T T M T Demand Γ(ff ν R ν R ) < H(T) T 2 /M Pl at BBN. 6 Mangano, Serpico, PLB (2011), [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 7/ 43

11 The Money Shot Unflavored Symmetries Unbroken B L Majorana B L Dirac B L 0 5 Log 10 Λ m q Ν BaBar BD Lim its on a B L force e Ν with Dirac neutrinos neutron BBN LEP LHC Log 10 g EP M g 100 GeV Casim ir Sun RG Ν ISR M g 10 9 GeV HB RG SN1987A Log 10 Α Log 10 M ev Applicable to any Z B L (BBN, RG/ν, solid SN1987 depend on number of light ν R). 7 7 J.H., arxiv: Julian Heeck Neutrinos and Abelian Gauge Symmetries 8/ 43

12 Majorana B L Unflavored Symmetries Unbroken B L Majorana B L Dirac B L New scalar φ B L=2 to break U(1) B L by two units. L Y ν ν R HL+ 1 2 Y R ν R ν c R φ B L=2 +h.c. Spontaneous symmetry breaking gives mass matrix for (ν L,νR c): ( ) 0 Y T M = ν H. Y ν H Y R φ B L=2 High scale Y R φ B L=2 Y ν H : small seesaw Majorana mass for active neutrinos: M ν H 2 φ B L=2 YT ν Y 1 R Y ν. Signature of Majorana B L: neutrinoless double beta decay (A,Z) (A,Z +2)+2e (B L) = 2. Julian Heeck Neutrinos and Abelian Gauge Symmetries 9/ 43

13 Majorana B L: Leptogenesis Unbroken B L Majorana B L Dirac B L L Y ν ν R HL+ 1 2 Y R ν R ν c R φ B L=2 +h.c. Heavy (M R Y R φ B L= GeV) Majorana neutrinos N = ν R +νr c decay out-of-equilibrium in early Universe. If CP violated in loops: Γ(N HL) Γ(N H L) Lepton asymmetry L! Sphalerons with B = L = 3 above T TeV transfer L to baryon asymmetry B. Julian Heeck Neutrinos and Abelian Gauge Symmetries 10/ 43

14 Dirac B L Unflavored Symmetries Unbroken B L Majorana B L Dirac B L Break B L, but by n 2 units. 8 Lepton number violating Dirac neutrinos. All fermions in SM+ν R are odd under B L only even (B L) possible. Lowest order new processes: (B L) = 4: O d=6 : ν c R ν R ν c R ν R O d=8 : H 2 ν c R ν R ν c R ν R, (L c H )( H L) ν c R ν R, F µν Y νc R σµνν R ν c R ν R O d=10 : (L c H )( H L) (L c H )( H L), H 2 (L c H )( H L) ν c R ν R, F µν Y (Lc H )( H L) ν c R σµνν R, W µν a (L c H )( H τ a L) ν c R σµνν R, (u R d c R )(d R H L)(ν c R ν R),... O d=18 : (d R dr c uc R u R e c R e R)(d R dr c uc R u R e c R e R),... [ O d=20 : ((D µl) c 2 H)(H D νl)] (e c L W µ + W ν + e L )(e c L W+µ W +ν e L ),... 8 Witten, hep-ph/ Julian Heeck Neutrinos and Abelian Gauge Symmetries 11/ 43

15 UV Completion Unflavored Symmetries Unbroken B L Majorana B L Dirac B L One scalar φ B L=4 to break B L, one scalar χ B L= 2 as mediator. L y αβ L α Hν R,β +κ αβ χ B L= 2 ν R,α νr,β c +h.c. Neutrinos are Dirac (and L = 2 forbidden) if χ B L= 2 = 0. Scalar potential V µφ B L=4 (χ B L= 2 ) 2 +h.c. Lepton number violation L = 4 still possible! 9 t Extension to left right model can enhance rates. 9 J.H. and W. Rodejohann, EPL 103, (2013) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 12/ 43

16 Unbroken B L Majorana B L Dirac B L Phenomenology of LNV Dirac Neutrinos How to check for L = 4? Collider processes: LHC: pp W W W W l + l + l + l + +X, Like-sign lepton collider: e e W W W W l + l +. Nuclear decays (0ν4β?). 10 Rare meson decays etc.? All tough, many particles in final state! (Even harder for L > 4...) L = 4 can however easily be relevant in the early Universe new Dirac leptogenesis mechanism! J.H. and W. Rodejohann, EPL 103, (2013) [arxiv: ]. 11 J.H., PRD 88, (2013) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 13/ 43

17 Dirac B L: Leptogenesis Unbroken B L Majorana B L Dirac B L Scalar potential V(H,φ,χ) µφ B L=4 (χ B L= 2 ) 2 breaks complex χ B L= 2 = (Ξ 1 +i Ξ 2 )/ 2 into two real scalars with mass m 2 1 = m 2 c 2µ φ B L=4, m 2 2 = m 2 c +2µ φ B L=4. Heavy mediator scalar Ξ j decays to ν R ν R or ν R ν R out-of-equilibrium in early Universe. Ξ i ν c R,δ Ξ j ν R,α + ν c R,δ Ξ j ν c R,γ ν R,β ν c R,γ CP violation requires second scalar χ B L= 2. Y νr nν R 1 ( Γ(Ξ i ν R ν R ) Γ Ξi νr c R) νc s g Γ(Ξ i ν R ν R )+Γ ( Ξ i νr c ). νc R Asymmetry in ν R. How to translate to baryon asymmetry? Julian Heeck Neutrinos and Abelian Gauge Symmetries 14/ 43

18 Baryon Asymmetry Unflavored Symmetries Unbroken B L Majorana B L Dirac B L Dirac-Yukawa coupling Y ν = m ν / H too small to equilibrate ν R... Add second scalar doublet H 2 with large Yukawa LH 2 ν R : Neutrinophilic H 2 with small VEV H 2 1eV. 12 Dirac neutrinos light with large Yukawas. H 2 moves Y νr to Y νl. Sphalerons move Y νl to Y B. Different from neutrinogenesis! Necessary thermalization of ν R N eff > 3! 3.14 N eff 3.29 depending on H 2 + mass and Yukawa coupling. Specific collider signatures of neutrinophilic H E. Ma, PRL 86 (2001), F. Wang, W. Wang, J. M. Yang, EPL 76 (2006), S. Gabriel and S. Nandi, PLB 655 (2007). 13 Davidson and Logan, PRD 80 (2009), arxiv: Julian Heeck Neutrinos and Abelian Gauge Symmetries 15/ 43

19 Unflavored Summary Unflavored Symmetries Unbroken B L Majorana B L Dirac B L name (B L) neutrino BAU signatures Unbroken B L 0 Dirac neutrinogenesis Z (?), N eff 3 Majorana B L 2 Majorana leptogenesis 0ν2β Dirac B L > 2, e.g. 4 Dirac Dirac leptogenesis 0ν4β, N eff 3.14 B L mystery: global, local, unbroken, broken by 2, 4,...units? Currently testing: L = 2 via 0ν2β. L 4 way more challenging (experimentally and theoretically). Lepton number violation not synonymous with Majorana neutrinos. L = 4 lowest LNV of Dirac neutrinos. New Dirac leptogenesis (3.14 N eff 3.29). Julian Heeck Neutrinos and Abelian Gauge Symmetries 16/ 43

20 Let s add some flavor... Neutrino Hierarchies Texture Zeros Neutrinos and abelian flavor symmetries flavored {}}{ U(1) B L U(1) Le L }{{} µ U(1) Lµ L τ }{{} unflavored dark. Julian Heeck Neutrinos and Abelian Gauge Symmetries 17/ 43

21 Neutrino Mixing Unflavored Symmetries Neutrino Hierarchies Texture Zeros Pontecorvo Maki Nakagawa Sakata leptonic mixing matrix c 12 c 13 s 12 c 13 e iα s 13 e i(β δ CP ) U = c 23 s 12 s 23 s 13 c 12 e iδ CP (c 23 c 12 s 23 s 13 s 12 e iδ CP)e iα s 23 c 13 e iβ s 23 s 12 c 23 s 13 c 12 e iδ CP (s 23 c 12 + c 23 s 13 s 12 e iδ CP)e iα c 23 c 13 e iβ with [Gonzalez-Garcia et al, arxiv: ] sin 2 θ , Normal Inverted sin 2 θ , m ev 2, ν 3 m 2 21 ν 2 ν 1 sin 2 θ (NO) or sin 2 θ (IO), m ev 2 (NO) or m ev 2 (IO). ν 2 ν 1 m 2 32 m 2 21 ν e ν µ ν τ m 2 31 ν 3 Ordering (normal or inverted), absolute scale, phases? Why these values? Symmetries!? Julian Heeck Neutrinos and Abelian Gauge Symmetries 18/ 43

22 Neutrino Hierarchies Unflavored Symmetries Neutrino Hierarchies Texture Zeros Majorana mass matrix M ν = Udiag(m 1,m 2,m 3 )U T in special cases: 1 Normal hierarchy (m 1 0) and best-fit values (phases zero): M ν ev 0 L e Inverted hierarchy (m 3 0) and α = π/2: M ν ev 0 0 L e L µ L τ Quasi-degenerate (m 1,2,3 1eV) and β = π/2: M ν ev 0 0 L µ L τ Julian Heeck Neutrinos and Abelian Gauge Symmetries 19/ 43

23 Now what? Unflavored Symmetries Neutrino Hierarchies Texture Zeros Three interesting zeroth order approximations: M Le ν 0, M Le Lµ Lτ ν , M Lµ Lτ ν [G. Branco, W. Grimus, L. Lavoura, NPB (1989); S. Choubey, W. Rodejohann, EPJC 40 (2005)] Impose U(1) X to get M X ν, then slightly break it. Goldstone boson... Here: promote to local symmetry. Goldstone massive Z. Remember: SM +3ν R has anomaly free U(1) B L U(1) Le L µ U(1) Lµ L τ. Simply take U(1) B 3Le, U(1) B+3(Le L µ L τ), or U(1) Lµ L τ? Julian Heeck Neutrinos and Abelian Gauge Symmetries 20/ 43

24 Wrong end of the seesaw Neutrino Hierarchies Texture Zeros Imposing U(1) B 3Le gives L e symmetric M R, but not L e symmetric because M Le R not invertible! Weird coincidence: M Le Lµ Lτ R M ν m T DM 1 R m D, ε 1 1 ε ε M ν M 1 ε R ε 2 ε ε L e L µ L τ gives approximate L e symmetry after seesaw! Broken U(1) B+3(Le L µ L τ) (say ε = 0.05) gives normal hierarchy. 14 (Inverted hierarchy requires additional Z 2 symmetry.) 14 J.H. and W. Rodejohann, PRD 85, (2012) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 21/ 43

25 Mixing Angles and Collider Neutrino Hierarchies Texture Zeros U(1) B+3(Le L µ L τ) broken by scalar S 6 in RHN sector: S ν c R,1ν R,1, S ν c R,2ν R,2, S ν c R,2ν R,3, S ν c R,3ν R,3 M R S. VEV v S ε M R gives: sin 2 Θ sin 2 Θ 13 µ and τ same U(1) charge: θ 23 random (large...). LEP-II constraint on U(1) B+3(Le L µ L τ): v S > 2.3TeV, LHC prospects in [H. S. Lee and E. Ma, PLB 688 (2010)]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 22/ 43

26 Neutrino Hierarchies Texture Zeros L µ L τ Anomaly free in SM even without ν R. 15. M Lµ Lτ invertible Seesaw gives L µ L τ symmetric M ν. Add one or two scalars S that couple to ν c R,i ν R,j and get a VEV. VEV fills zeros in M R and M ν and gives mass to Z boson M Z /g S. No Z coupling to first generation Weak limits for heavy Z : M Z /g > 550GeV at 95% C.L. from trident production at CCFR ν µ N ν µ N ν µ Nµ + µ. 16 Light Z (below 400MeV) can resolve muon s magnetic moment anomaly Foot (1991), He, Joshi, Lew, Volkas (1991). 16 Altmannshofer Gori, Pospelov, Yavin, PRD 89 (2014) [arxiv: ]. 17 Altmannshofer Gori, Pospelov, Yavin, PRL 113 (2014) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 23/ 43

27 Neutrino Hierarchies Texture Zeros L µ L τ Two scalars, ε = v S / M R = 0.02: 0.36 sin 2 Θ sin 2 Θ sin 2 Θ 13 sin 2 Θ 13 Julian Heeck Neutrinos and Abelian Gauge Symmetries 24/ 43

28 Neutrino Hierarchies Texture Zeros L µ L τ and Lepton Flavor Violation LFV in charged leptons if we break L µ L τ with a scalar doublet. 18 Can source h µτ. 19 SM-like doublet Φ 2, new doublet Φ 1 with L µ L τ charge 2, and singlet S with +1: V(Φ 1,Φ 2,S) = m 2 1 Φ λ 1 2 Φ 1 4 m 2 2 Φ λ 2 2 Φ 2 4 +λ 3 Φ 1 2 Φ 2 2 +λ 4 Φ 1 Φ2 2 µ 2 S S 2 + λ S 2 S 4 +λ Φ1 S Φ 1 2 S 2 +λ Φ2 S Φ 2 2 S 2 δ S 2 Φ 2Φ1 +h.c. S heavy and large VEV: 2HDM with softly broken U(1): V(Φ 1,Φ 2) m 2 1 Φ λ 1 2 Φ 1 4 m 2 2 Φ λ 2 2 Φ 2 4 +λ 3 Φ 1 2 Φ 2 2 +λ 4 Φ 1 Φ2 2 m3φ 2 2Φ1 +h.c. Small VEV for Φ 1 : Φ 1 Φ 2 m 2 3 /m2 1 δ Φ 2 S 2 /m J.H., Rodejohann, PRD 84 (2011) [arxiv: ]. 19 J.H., Holthausen, Rodejohann, Shimizu, arxiv:1411.xxxx. Julian Heeck Neutrinos and Abelian Gauge Symmetries 25/ 43

29 Yukawa Structure Unflavored Symmetries Neutrino Hierarchies Texture Zeros L Y = L L Y l1 Φ 1 l R +L L Y N1 Φ 1 N R with matrices +L L Y l2 Φ 2 l R +L L Y N2 Φ 2 N R +Q L Y u Φ 2 u R +Q L Y d Φ 2 d R Nc RM N N R Nc RY S1 SN R Nc RY S2 SN R +h.c. Y l2 = diag(y e,y µ,y τ ), Y N2 = diag(y 1,y 2,y 3 ), Y l1 = 0 0 0, Y N1 = 0 0 ξ ξ τµ a 13 0 a 12 0 M N = M M 2,Y S1 = 0 0 0, Y S2 = a a M 2 Julian Heeck Neutrinos and Abelian Gauge Symmetries 26/ 43

30 Charged Lepton Masses Neutrino Hierarchies Texture Zeros M e = v 2 y e s β y µ s β ξ τµ c β y τ s β V el diag(m e,m µ,m τ )V e R, with tanθ L tanθ R = m µ m τ 1 and sinθ R v m τ ξ τµ 2 cosβ. SM-like scalar h couples y diag(m e,m µ,m τ ) c α vs β } {{ } type-i 2HDM s R m τ v cos(α β) c β s β 0 c R s L s L s R c L c R c L s R. Only LFV in µ τ sector, quarks and electrons save! Julian Heeck Neutrinos and Abelian Gauge Symmetries 27/ 43

31 h µτ Unflavored Symmetries Neutrino Hierarchies Texture Zeros S S Φ2 S S τ Φ1 µ µ + Φ2 τ Φ2 Φ1 τ CMS 2.5σ excess in h µτ for 20 yτµ h = mτ v cos(α β) c β s β c R c L s R cos(α β) s β c β c R s R! Either c β,s R 1 and ξ τµc α β , or larger s R and correlations with h ττ, µµ: ( ) 2 BR(h ττ) cα y h v τµ t R (1±0.4 t R ) 2, BR(h ττ) SM s β m τ compared to 0.78±0.27 (CMS) or (ATLAS). 20 J.H., Holthausen, Rodejohann, Shimizu, arxiv:1411.xxxx. Julian Heeck Neutrinos and Abelian Gauge Symmetries 28/ 43

32 One step further: texture zeros Neutrino Hierarchies Texture Zeros U(1) B L U(1) Le L µ U(1) Lµ L τ subgroups forbid entries in M R texture zeros! 21 Choose subgroup so that some entries are allowed, others filled by S, e.g. B L e +L µ 3L τ with Y (S) = 2: M R = M S M 1 ν. 0 Dirac matrices diagonal by symmetry, so M R M 1 ν. Texture zeros imply testable correlations among neutrino parameters, seven out of 15 two-zero patterns currently viable. 21 J.H., Araki, Kubo, JHEP 1207 (2012) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 29/ 43

33 Neutrino Hierarchies Texture Zeros Simplest U(1) models with just one scalar With just one scalar S, we can get five of the seven valid patterns: 22 Symmetry generator Y Y (S) Texture zeros in M R Texture zeros in M ν L µ L τ 1 (M R ) 33, (M R ) 22 (C R ) B L e +L µ 3L τ 2 (M R ) 33, (M R ) 13 (B R 4 ) (Mν) 12, (M ν) 22 (B ν 3 ) B L e 3L µ +L τ 2 (M R ) 22, (M R ) 12 (B R 3 ) (Mν) 13, (M ν) 33 (B ν 4 ) B +L e L µ 3L τ 2 (M R ) 33, (M R ) 23 (D R 2 ) (Mν) 12, (M ν) 11 (A ν 1 ) B +L e 3L µ L τ 2 (M R ) 22, (M R ) 23 (D R 1 ) (Mν) 13, (M ν) 11 (A ν 2 ) Many patterns are hard to distinguish via neutrino experiments, e.g. D R 1 and D R 2, but the symmetries B +L e 3L µ L τ and B +L e L µ 3L τ are very different new possibilities to disentangle texture zeros. More scalars or discrete Z N subgroups can generate other allowed patterns. 22 J.H., Araki, Kubo, JHEP 1207 (2012) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 30/ 43

34 Flavored Summary SM+3ν R has anomaly free local U(1) B L U(1) Le L µ U(1) Lµ L τ. Can use subgroups to influence Neutrino hierarchies: U(1) B+3(Le L µ L τ) for normal hierarchy, (U(1) B+3(Le L µ L τ) Z 2 for inverted hierarchy,) U(1) Lµ L τ for quasi-degenerate. Texture zeros in M ν or M 1 ν. Specific LFV modes, e.g. h µτ via L µ L τ. (Z pheno on top: muon s magnetic moment, leptophilic DM,...) Very simple models, surprisingly potent framework! Julian Heeck Neutrinos and Abelian Gauge Symmetries 31/ 43

35 Sterile Neutrinos Dark Matter and Light Sterile Neutrinos Neutrinos and dark gauge symmetries flavored {}}{ U(1) B L U(1) Le L }{{} µ U(1) Lµ Lτ }{{} unflavored dark. LSND, MiniBooNE: ν S with ev mass and mixing U as 0.1? Tension appearance vs. disappearance... Tension with cosmology... [Kopp, Neutrino 2014] If we ever observe a sterile neutrino, it s lighter than expected (10 9 GeV). Why? Julian Heeck Neutrinos and Abelian Gauge Symmetries 32/ 43

36 How to make ν s light? Unflavored Symmetries Sterile Neutrinos Dark Matter Isn t new physics always at TeV? Use seesaw partners ν R as steriles: ev-seesaw ( ) 0 md M = m T D M R with m D 0.1eV, M R 1eV. [de Gouvêa, PRD (2005)] Active sterile mixing automatically large: U as m D /M R m ν /m s 0.1. Minimal 3+2 scheme: two ν R at ev scale, works fine. [Donini, Schwetz et al., JHEP (2012)] Just throw in random O(1) couplings: sterile neutrino anarchy. [JH, Rodejohann, PRD (2013)] The heavy ev-scale suppresses the light 0.1 ev? Julian Heeck Neutrinos and Abelian Gauge Symmetries 33/ 43

37 How to make ν s light? II Sterile Neutrinos Dark Matter Put ν s on the other side of the seesaw: ν α ν s ν R Suppressed BY seesaw: need additional right-handed singlet S and mass matrix for (ν α, ν c R,j, Sc ) 0 m D 0 M MES = md T M R m S. 0 ms T 0 Minimal Extended Seesaw (MES) [Chun, Joshipura, Smirnov, PLB (1995), Babu, Seidl, PRD,PLB (2004), Barry, Rodejohann, Zhang, JHEP (2011), Zhang, PLB (2012)] Works also for 3+2, 3+3,..., just add more singlets. Julian Heeck Neutrinos and Abelian Gauge Symmetries 34/ 43

38 Minimal extended seesaw Sterile Neutrinos Dark Matter m D 0 M MES = md T M 3 3 R m S 0 ms T Assume M R m D,m S, usual seesaw: ( (md M 1 R mt D )3 3 M 4 4 ν m T S M 1 R mt D m D M 1 R m S (m T S M 1 R m S) 1 1 ). all masses suppressed by seesaw scale M R GeV. sterile mass m 4 1 ev for m S 5 10m D. active sterile mixing U as = O(m D /m S ) automatically right. SBL sterile neutrinos. Great, but how to get MES structure? Julian Heeck Neutrinos and Abelian Gauge Symmetries 35/ 43

39 How to get MES Unflavored Symmetries Sterile Neutrinos Dark Matter Need and forbid couplings L H ν R, m S S c ν R, M R ν c R ν R L H S, S c S. Flavor symmetry A 4 Z 4 (messy...). [Zhang, PLB (2012)] Abelian gauge symmetry U(1) : simple, but need additional fermions to cancel anomalies. [Babu, Seidl, PLB (2004)] Cancel anomalies, make new fermions massive, and not disturb MES structure? With few scalars? Yes! Julian Heeck Neutrinos and Abelian Gauge Symmetries 36/ 43

40 Magic numbers Unflavored Symmetries Sterile Neutrinos Dark Matter ν R,1 ν R,2 ν R,3 S 1 S 2 S 3 S 4 S 5 S 6 S 7 φ Y Mass matrix has nice block structure: ( ) (MMES ) M = (M S ) 6 6 with 0 y 1 φ y 1 φ M S = y 2 φ y 2 φ y 3 φ y 3 φ 0. S 1 gives MES, S 2,3,4,5,6,7 decouple and form 3 Dirac fermions Ψ 1,2,3! Julian Heeck Neutrinos and Abelian Gauge Symmetries 37/ 43

41 More numbers Unflavored Symmetries Sterile Neutrinos Dark Matter Happy accident : φ breaks U(1) to Z 11. all three Ψ j stable! Active sterile mixing V 4j O(m D /m S )! = O(0.1). For O(1) Yukawas U(1) breaking at φ 10 H TeV. masses for Z, Re(φ), Ψ 1,2,3 around 100GeV TeV. Multicomponent stable dark matter. Breakdown of neutral fermions: seesaw/leptogenesis Ψ 1 {}}{{}}{{}}{{}}{ ν e,ν µ,ν τ,s 1, ν R,1,ν R,2,ν R,3, S 2,S 3, S 4,S 5, S 6,S }{{}}{{} 7 (3+1) MES DM Ψ 2 Ψ 3 Julian Heeck Neutrinos and Abelian Gauge Symmetries 38/ 43

42 Dark matter interactions Sterile Neutrinos Dark Matter Lagrangian: ( [iψ j γ µ µ Ψ j M j 1+ Re(φ) ) Re(φ) j Ψ j Ψ j + g 2 Z µψ j γ µ( g V j +g A j γ 5 ) Ψj ] with g V 1 = 1, gv 2 = 13, gv 3 = 7, ga 1 = 11, ga 2 = 11, ga 3 = 11. Connection to the Standard Model just like all other U(1) DM models: Scalar mixing (Higgs portal): L δ H 2 φ 2 Ψ j couple to Brout Englert Higgs boson. Vector mixing (kinetic-mixing portal): L sinξ F µν Y F µν Ψ j couple to Z boson. New: Fermion mixing (neutrino portal): L 11g 2 Z µ i,j=1 4 V4iV 4j (ν i γ µ γ 5 ν j +ν i γ µ ν j ). Julian Heeck Neutrinos and Abelian Gauge Symmetries 39/ 43

43 Neutrino portal Unflavored Symmetries Sterile Neutrinos Dark Matter M R GeV ν R,j φ Z, φ DM : Ψ i Ψ j TeV Z Z H φ H 100 GeV SM Z ev W, Z ν α V 4j ν s Julian Heeck Neutrinos and Abelian Gauge Symmetries 40/ 43

44 Relic density via neutrino portal Sterile Neutrinos Dark Matter Relic density via annihilation ΨΨ Z ν s ν s into sterile neutrinos M = M = M = 800 GeV M = 500 GeV M = 600 GeV M = 800 GeV 10 0 M = 1 TeV M = 500 GeV h h M Z' [GeV] M Z' [GeV] Direct detection is loop-suppressed: m 2 41 /(100GeV) Indirect detection: BR(ΨΨ νν) 100% gives monochromatic neutrinos from Galactic halo. Too small for IceCube... Including Higgs portal and kinetic-mixing portal gives the usual measurable effects. Julian Heeck Neutrinos and Abelian Gauge Symmetries 41/ 43

45 Dark Summary Unflavored Symmetries Sterile Neutrinos Dark Matter Additional right-handed neutrinos with exotic charges under a broken U(1) can generate structure in neutral fermions. Here: generate seesaw-suppressed sterile neutrino. Magic numbers: necessary anomaly-cancelling fermions form multicomponent DM. Gauge interactions open new SM DM portal through sterile neutrinos. Huge unexplored playground! Other charges: 3+2, 3+3, Majorana DM, unstable DM,... Julian Heeck Neutrinos and Abelian Gauge Symmetries 42/ 43

46 Conclusion Unflavored Symmetries Sterile Neutrinos Dark Matter Abelian gauge symmetries U(1) versatile framework. Simple, minimalistic, renormalizable. SM-motivated symmetries flavored {}}{ U(1) B L U(1) Le L }{{} µ U(1) Lµ L τ }{{} unflavored dark connected to neutrino properties: B L for Majorana vs. Dirac and leptogenesis. B L only possible unbroken symmetry acting on SM particles. L µ L τ, B +3(L e L µ L τ),...for hierarchies, mixing angles, texture zeros, LFV, h µτ, muon s magnetic moment, R-parity,... Dark U(1) for sterile neutrino pheno, dark matter stability and abundance,.... Julian Heeck Neutrinos and Abelian Gauge Symmetries 43/ 43

47 Conclusion Unflavored Symmetries Sterile Neutrinos Dark Matter Abelian gauge symmetries U(1) versatile framework. Simple, minimalistic, renormalizable. SM-motivated symmetries flavored {}}{ U(1) B L U(1) Le L }{{} µ U(1) Lµ L τ }{{} unflavored dark connected to neutrino properties: B L for Majorana vs. Dirac and leptogenesis. B L only possible unbroken symmetry acting on SM particles. L µ L τ, B +3(L e L µ L τ),...for hierarchies, mixing angles, texture zeros, LFV, h µτ, muon s magnetic moment, R-parity,... Dark U(1) for sterile neutrino pheno, dark matter stability and abundance,... Merci! Julian Heeck Neutrinos and Abelian Gauge Symmetries 43/ 43.

48 How to check for L = 4? Sterile Neutrinos Dark Matter Neutrinoless quadruple beta decay 23 (A,Z) (A,Z +4)+4e e.g. via O L=4 = (ν c L ν L) 2 /Λ 2 : d d u u W e ν ν ν ν W e e e d u d u Collider process e e W W W W l + l +. Rare meson decays etc.? 23 J.H. and W. Rodejohann, EPL 103, (2013) [arxiv: ]. Julian Heeck Neutrinos and Abelian Gauge Symmetries 44/ 43

49 Candidate Nuclei for 0ν4β Sterile Neutrinos Dark Matter Q 0ν4β Other decays NA/% 96 40Zr 96 44Ru MeV τ 2ν2β 1/ y Xe Ce MeV τ 2ν2β 1/ y Nd Gd MeV τ 2ν2β 1/ y 5.6 Q0ν4β Mass 2β 0ν4β 2β + Z 0 2 Z 0 Z 0 +2 Z Julian Heeck Neutrinos and Abelian Gauge Symmetries 45/ 43

50 Sterile Neutrinos Dark Matter Best Candidate: Neodymium 150 Nd Decay channels: Nd Sm via 2ν2β (τ 2ν2β 1/ y): the two electrons have a continuous energy spectrum and total energy E e,1 +E e,2 < 3.371MeV Nd Gd via 0ν4β. Four electrons with continuous energy spectrum and summed energy Q 0ν4β = 2.079MeV are emitted. In this special case, the daughter nucleus is α-unstable with half-life τ1/2( α Gd Sm) y. Decay rate 2ν2β 0ν4β 0ν2β Q 0ν4β Q 0ν2β Energy 0ν4β kinematically allowed, but expected rates unobservable. Julian Heeck Neutrinos and Abelian Gauge Symmetries 46/ 43

51 Texture Zeros Unflavored Symmetries Sterile Neutrinos Dark Matter Take M ν and set two independent entries to zero four constraints on the nine low-energy parameters (m 1,m 2,m 3 ), (θ 23,θ 12,θ 13 ) and (δ,α,β) (CP violating phases) 15 two-zero textures possible, only 7 allowed at 3σ: [H. Fritzsch et al, JHEP 1109 (2011)] A ν 1 : 0 0 0, A ν 2 : 0 0, B ν 1 : 0 0, B ν 2 : 0 0, B ν 3 : 0 0 0, B ν 4 : 0, C ν : Julian Heeck Neutrinos and Abelian Gauge Symmetries 47/ 43

52 Vanishing Minors Unflavored Symmetries Sterile Neutrinos Dark Matter Same idea, but with M 1 ν instead of M ν. Seven patterns for M 1 ν allowed: D R 1 : 0 0, D R 2 : 0, B R 3 : 0 0, B R 4 : 0, 0 0 B R 1 : 0 0, B R 2 : 0, C R : Two-zero texture in M 1 ν corresponds to two vanishing minors in M ν. E.g. 0 M 1 = 0 0 M 11 M 13 M 31 M 33 = 0 = M 21 M 22 M 31 M 32 Julian Heeck Neutrinos and Abelian Gauge Symmetries 48/ 43